Title :
Stability analysis of fluid flows using sum-of-squares
Author :
Goulart, P.J. ; Chernyshenko, S.I.
Author_Institution :
Dept. of Aeronaut., Imperial Coll. London, London, UK
fDate :
June 30 2010-July 2 2010
Abstract :
In this paper we present a new method for assessing the stability of finite-dimensional approximations to the Navier-Stokes equation for fluid flows. Approximations to the Navier-Stokes equation typically take the form of a set of linear ODEs with an additional bilinear term that conserves the total energy of the system state. We suggest a structured method for generating Lyapunov functions using sum-of-squares optimization that exploits this energy conservation property. We provide a numerical example demonstrating the use of this technique to assess the stability of a model of a shear flow between infinite parallel plates.
Keywords :
Lyapunov methods; Navier-Stokes equations; flow instability; flow simulation; linear differential equations; optimisation; shear flow; Lyapunov functions; Navier-Stokes equation; bilinear term; energy conservation property; finite-dimensional approximations; fluid flows; infinite parallel plates; linear ODE; shear flow model; stability analysis; structured method; sum-of-square optimization; system state; total energy; Boundary conditions; Differential equations; Energy conservation; Fluid flow; Fluid flow control; Lyapunov method; Navier-Stokes equations; Optimization methods; Polynomials; Stability analysis;
Conference_Titel :
American Control Conference (ACC), 2010
Conference_Location :
Baltimore, MD
Print_ISBN :
978-1-4244-7426-4
DOI :
10.1109/ACC.2010.5531305
